Fast Multigrid Solvers for Transport with Forward-Peaked Scattering

用于具有前向峰值散射传输的快速多重网格求解器

• 批准号: 1015370
• 负责人: Scott MacLachlan
• 金额: $ 27.95万
• 依托单位: Tufts University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-09-01 至 2014-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1015370&HistoricalAwards=false
• 关键词: Fast; Multigrid; Solvers; Transport; Forward

The primary goal of this proposal is to develop fast, efficient, and robust multigrid-based solvers for the solution of the linear Boltzmann-transport equation in the regime of highly forward-peaked scattering. Recently, the project team have developed an angular multigrid algorithm for a model problem that captures the essential features of the Boltzmann-transport equation for scattering in a two-dimensional "Flatland" model. The research goals of this project are, thus, to extend this approach to an efficient and effective method for true three-dimensional scattering, in realistic media, with accurate discretizations. Among the challenges of extending the already developed technique to three dimensions are improving the discretization to allow discontinuous coefficients, and local grid refinement needed in regions of interest. Additionally, the project team will investigate theoretical analysis of the convergence of these algorithms, in both two and three spatial dimensions, providing critical insight into the design of these algorithms for realistic scattering kernels.Accurate and efficient models of forward-peaked scattering are of significant interest in both biomedical and nuclear engineering applications. This regime describes the scattering of electron beams, used in radiation therapy for the treatment of certain cancerous tumors, as well as the transport of charged particles in reactor physics and astrophysics. While there is a long history of interest in efficient and accurate algorithms for modeling charged-particle transport, the problem still poses formidable challenges. The approach considered here offers a new direction for research in this area. The proposed work leads directly to simulation tools for biomedical and nuclear engineers and scientists. The active roles of the PI and co-PI in the computational science and mathematical biology communities ensure timely and widespread dissemination of the resulting algorithms. Furthermore, the project directly involves a doctoral student, who is actively mentored by the PI and co-PI, contributing to the training of an early career scientist in an important field of research.

这个建议的主要目标是开发快速，高效，强大的基于多重网格的求解器的线性玻尔兹曼输运方程的解决方案，在政权的高度向前峰散射。 最近，该项目小组已经开发了一个角度多重网格算法的模型问题，捕捉的玻尔兹曼输运方程的散射在一个二维的“平面”模型的基本特征。 因此，本项目的研究目标是将这种方法扩展为一种高效和有效的方法，用于真实的三维散射，在现实的介质中，具有精确的离散化。 将已经开发的技术扩展到三维的挑战包括改进离散化以允许不连续系数，以及感兴趣区域需要局部网格细化。 此外，项目团队将调查这些算法的收敛性的理论分析，在两个和三个空间维度，提供关键的洞察这些算法的设计，为现实的散射kernels.Accurate和高效的模型前向峰值散射在生物医学和核工程应用的重大利益。 该机制描述了电子束的散射，用于治疗某些癌症肿瘤的放射治疗，以及反应堆物理学和天体物理学中带电粒子的传输。 虽然有一个长期的历史感兴趣的有效和准确的算法建模带电粒子输运，这个问题仍然构成了巨大的挑战。 这里考虑的方法在这一领域的研究提供了一个新的方向。 拟议的工作直接导致生物医学和核工程师和科学家的模拟工具。 PI和co-PI在计算科学和数学生物学社区中的积极作用确保了所产生的算法的及时和广泛传播。 此外，该项目直接涉及一名博士生，他由PI和co-PI积极指导，有助于在重要的研究领域培养早期职业科学家。